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trasher [3.6K]
3 years ago
5

Work out the length of the following rectangles

Mathematics
1 answer:
tiny-mole [99]3 years ago
8 0

(a) a = 10.9 cm

(b) b = 20.78 cm

(c) c = 4.06 cm

<u>Explanation:</u>

(a)

height, h = 5cm

Hypotenuse, H = 12cm

Base, a = ?

Using pythagoras theorm:

(H)² = (h)² + (a)²

(12)² = (5)² + (a)²

119 = a²

a = 10.9 cm

(b)

Hypotenuse, H = 24 cm

Base, a = 12 cm

Height, b = ?

Using pythagoras theorm:

(H)² = (b)² + (a)²

(24)² = (b)² + (12)²

432 = b²

b = 20.78 cm

(c)

height, h = 4 cm

Hypotenuse, H = 5.7 cm

Base, c = ?

Using pythagoras theorm:

(H)² = (h)² + (c)²

(5.7)² = (4)² + (c)²

16.49 = c²

c = 4.06 cm

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Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement.
Mrrafil [7]

Answer:

E(X_n)=\frac{2(n-1)}{27}

E(y)=\frac{14}{9}

Step-by-step explanation:

From the question we are told that:

Sample size n=9

Number of Green g=4

Number of yellow y=4

Number of white w=4

Probability of Green Followed by yellow P(GY) ball

 P(GY)=\frac{4}{9}*\frac{3}{9}

 P(GY)=\frac{4}{27}

Generally the equations for when n is even is mathematically given by

 Probability of success P(S)=\frac{4}{27}

 Probability of Failure P(F)=\frac{27-4}{27}

 Probability of Failure P(F)=\frac{23}{27}

Therefore

 E(X_n)=\frac{n}{2}*P

 E(X_n)=\frac{n}{2}*\frac{4}{27}

 E(X_n)=\frac{2n}{27}

Generally the equations for when n is odd is mathematically given by

 \frac{n-1}{2}

 E(X_n)=\frac{n-1}{2}*\frac{4}{27}

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b)

Probability of drawing white ball

 P(w)=\frac{2}{9}

Therefore

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Therefore

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 E(y)=[\frac{9}{2}-1]\frac{4}{9}

 E(y)=\frac{14}{9}

5 0
3 years ago
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Elodia [21]
First, let's only the expression with x stay on the let side: let's add 9 to both sides of the equation.

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